We report on polarization-resolved resonant photoluminescence (PL) spectroscopy of bright (spin-1) and dark (spin-2) excitons in colloidal CdSe nanocrystal quantum dots. Using high magnetic fields to 33 T, we resonantly excite (and selectively analyze PL from) spin-up or spin-down excitons. At low temperatures (<4K) and above ~10 T, the spectra develop a narrow, circularly polarized peak due to spin-flipped bright excitons. Its evolution with magnetic field directly reveals a large (1-2 meV), intrinsic fine structure splitting of bright excitons, due to anisotropic exchange. These findings are supported by time-resolved PL studies and polarization-resolved PL from single nanocrystals.